Multi-Scale and Finite Element Analysis of the Mixed Boundary Value Problem in a Perforated Domain under Coupled Thermoelasticity

2005 ◽  
Vol 9 ◽  
pp. 153-162
Author(s):  
Yongping Feng ◽  
Junzhi Cui
Keyword(s):  
Finite Element ◽  
Mixed Boundary ◽  
Asymptotic Expression ◽  
Perforated Domain ◽  
Scale Analysis ◽  
Element Analysis ◽  
Coupled Thermoelasticity ◽  
Multi Scale ◽  
Error Estimations ◽  
Small Periodic

The two-scale asymptotic expression and error estimations based on two-scale analysis (TSA) are presented for the solution of the increment of temperature and the displacement of a composite structure with small periodic configurations under coupled thermoelasticity condition in a perforated domain. The two-scale coupled relation between the increment of temperature and displacement is established.The multi-scale finite element algorithms corresponding to TSA are described and numerical results are presented.

scholarly journals Homogenization of trabecular structures

2020 ◽  
Vol 310 ◽  
pp. 00041
Author(s):  
Tomáš Krejčí ◽  
Aleš Jíra ◽  
Luboš Řehounek ◽  
Michal Šejnoha ◽  
Jaroslav Kruis ◽  
...  
Keyword(s):  
Finite Element ◽  
Effective Properties ◽  
Macro Level ◽  
Truss Structures ◽  
Scale Analysis ◽  
Scale Problem ◽  
Meso Level ◽  
Multi Scale ◽  
Macro Scale ◽  
Multi Scale Analysis

Numerical modeling of implants and specimens made from trabecular structures can be difficult and time-consuming. Trabecular structures are characterized as spatial truss structures composed of beams. A detailed discretization using the finite element method usually leads to a large number of degrees of freedom. It is attributed to the effort of creating a very fine mesh to capture the geometry of beams of the structure as accurately as possible. This contribution presents a numerical homogenization as one of the possible methods of trabecular structures modeling. The proposed approach is based on a multi-scale analysis, where the whole specimen is assumed to be homogeneous at a macro-level with assigned effective properties derived from an independent homogenization problem at a meso-level. Therein, the trabecular structure is seen as a porous or two-component medium with the metal structure and voids filled with the air or bone tissue at the meso-level. This corresponds to a two-level finite element homogenization scheme. The specimen is discretized by a reasonable coarse mesh at the macro-level, called the macro-scale problem, while the actual microstructure represented by a periodic unit cell is discretized with sufficient accuracy, called the meso-scale problem. Such a procedure was already applied to modeling of composite materials or masonry structures. The application of this multi-scale analysis is illustrated by a numerical simulation of laboratory compression tests of trabecular specimens.

Sign in / Sign up

Export Citation Format

Share Document